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Hypersonic waveriders have a large flight envelope, leading to the difficulty in keeping overall flight stability for a fixed geometry. Accordingly, hypersonic waveriders can be considered to design as a morphing vehicle such that the flight range is expanded for waveriding stability. To this end, this paper investigates the collaborative deformation design using control integrated analysis methods for the hypersonic waverider. Firstly, a parametric model is applied to combine the shape deformation with the geometrical properties. Secondly, the morphing process with regard to the change in a single geometric parameter and the static and dynamic characteristics affected by this deformation are analyzed. Afterwards, the collaborative relations are discussed for the changes in the lower forebody angle and elevon area. Furthermore, a flight control law is designed to guarantee flight stability while implementing the collaborative deformation, and the morphing results are evaluated based on the control-oriented idea. Finally, a simulation example is used to verify the effectiveness of the proposed methods for the hypersonic waverider.

Interest in hypersonic vehicles has origins in two main applications. The first is to provide a reliable and cheap way to space. The second is to realize a fast response to potential threats around the globe [

Recently, the trade-off studies are paid more attention for the control-oriented design of hypersonic vehicles. This is due to the presence of the complex interactions in a hypersonic vehicle, involving aerodynamics, propulsion, control, and so on. Meanwhile, the highly integrated dynamics of the hypersonic vehicle require a tightly integrated design process [

Morphing air vehicles are a concept that uses geometric changes to adapt to multipoint mission environments and improve overall performance [

This paper will investigate the design problems with respect to the collaborative deformation using the control integrated methods for hypersonic waverider. First, a parametric model is built using hypersonic aerodynamic theories for acquiring the coupling relations between the deformation and flight dynamics. Second, a trade-off design is studied based on the static and dynamic characteristics. Furthermore, the collaborative deformations are investigated to realize the matched design with regard to the multidiscipline contents, and at the same time a flight control law is designed to suppress the uncertain disturbances in the morphing process. Finally, a simulation example is provided to verify the feasibility of the proposed methods for hypersonic vehicles.

The first work for conducting the collaborative deformation design is to establish the parametric model of hypersonic vehicles, involving the aerodynamic module, propulsive module, control module, structure module, and so on. These modules are strong coupling each other, and the mutual influence makes the nonlinear model exhibit the unstable, nonminimum, and time-varying features. Therefore, the exact description on these coupling relations is critical for hypersonic vehicles to understand their inherent dynamic characteristics, determining the control design space and feasible flight range. To obtain the parametric model, this paper uses a typical waverider structure, shown in Figure

Typical waverider structure of hypersonic vehicles.

When the airflow enters into the lower forebody, the oblique shock wave theories are applied to estimate the shock angle

Accordingly, the pressures can be gotten for all surfaces in Figure

Besides these aerodynamic forces, the propulsive force is necessary to be estimated for establishing the parametric model, and the according propulsive structure is shown in Figure

Propulsive structure.

This paper applies a 2D inlet model shown, and the combustion chamber is assumed as the average cross section. In this case, the airflow parameters in the combustion chamber, including the flight Mach

If

Correspondingly, the lift due to the propulsive action is computed by

Furthermore, based on the matching relations of the aerodynamic forces in Figure

Matching relations of aerodynamic forces.

Based on the acquired data, the trust region method is used to regulate these parameters for the curve-fitted expressions. In principle, it is expected that the fitting errors are small for the purpose of achieving the satisfactory matching relationship between the estimated data and the obtained fitting expressions. Under normal circumstances, the maximum standard residual index is provided to test this matching relation, and it is expressed by

The Taylor expansion is used for the nonlinear model in (

Furthermore, according to (

Accordingly, the sensitivity function of flight performances with respect to these morphing variables is shown as [

Obviously, the larger

Afterwards, the nonlinear model is transformed into the following equivalent linear model [

Based on (

Correspondingly, the overall study configuration is given for the collaborative deformation design in Figure

Overall study configuration of collaborative deformation design.

Compared with the approaches and results in [

In the simulation, this paper uses the given geometric parameters of hypersonic waverider in [

Based on that, we first consider the change in the single shape parameter including the lower forebody angle and elevon area, and when the lower forebody angle changes from 3 deg to 6 deg, the change curves of the trim angle of attack and control inputs are provided in Figure

Trim angle of attack and control inputs with respect to lower forebody angle change.

Figure

Trim angle of attack and control inputs with respect to elevon area change.

Figure

Collaborative relations between lower forebody angle change and elevon area change.

Figure

Furthermore, the inversion control law is applied to ensure flight stability and realize the command track. In the simulation, the command signals include

Response curves with respect to given command signals.

Figure

Changes in the angle of attack and control inputs.

Figure

This paper investigates the collaborative deformation design problems for the hypersonic waverider. Although the typical structure of a hypersonic vehicle is used, the active deformation is considered with the changes in the lower forebody angle and elevon area. In addition, a control-related design framework is proposed for analyzing the effectiveness of the collaborative deformation of the hypersonic waverider, and this framework involves the multidisciplinary approaches, including aerodynamics, propulsion, and control. Furthermore, a simulation example is given to demonstrate that the collaborative deformation design is necessary to acquire the satisfactory performance through the overall envelope for the hypersonic waverider. We believe this work will be helpful to develop novel aerospace vehicles in the future.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by National Natural Science Foundation of China under Grant no. 61403191, the open funding project of State Key Laboratory of Virtual Reality Technology and Systems under Grant nos. BUAA-VR-14KF-03 and BUAA-VR-14KF-06, and Natural Science Foundation of Jiangsu Province under Grant no. BK20130817. The authors thank the editors and the reviewers for their help and improvements to the quality of our presentation.